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4. TITLE AND SUBTITLE Thermophysical Properties of Energetic Ionic Liquids/Nitric Acid Mixtures: Insights from Molecular Dynamics Simulations

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6. AUTHOR(S) Justin B. Hooper, Grant D. Smith, and Dmitry Bedrov

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14. ABSTRACT Molecular dynamics (MD) simulations of mixtures of the room temperature ionic liquids (ILs) 1-butyl-4 methyl imidazolium [BMIM]/dicyanoamide [DCA] and [BMIM][NO3--‐] with HNO3 have been performed utilizing the polarizable, quantum chemistry based APPLE&P® potential. Experimentally it has been observed that [BMIM][DCA] exhibits hypergolic behavior when mixed with HNO3 while [BMIM][NO3--‐] does not. The structural, thermodynamic and transport properties of the IL/HNO3 mixtures have been determined from equilibrium MD simulations over the entire composition range (pure IL to pure HNO3) based on bulk simulations. Additional (non--‐equilibrium) simulations of the composition profile for IL/HNO3 interfaces as a function of time have been utilized to estimate the composition dependent mutu al diffusion coefficients for the mixtures. The latter have been employed in continuum--‐level simulations in order to examine the nature (composition and width) of the IL/HNO3 interfaces on the millisecond time scale.

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1

Thermophysical Properties of Energetic Ionic Liquids/Nitric Acid Mixtures:

Insights from Molecular Dynamics Simulations

Justin B. Hooper, Grant D. Smith, and Dmitry Bedrov

Wasatch Molecular, Incorporated

825 N. 300 W., Salt Lake City, UT 84103

Abstract

Molecular dynamics (MD) simulations of mixtures of the room temperature ionic liquids (ILs) 1-‐

butyl-‐4-‐methyl imidazolium [BMIM]/dicyanoamide [DCA] and [BMIM][NO3-‐] with HNO3 have been

performed utilizing the polarizable, quantum chemistry based APPLE&P® potential.

Experimentally it has been observed that [BMIM][DCA] exhibits hypergolic behavior when mixed

with HNO3 while [BMIM][NO3-‐] does not. The structural, thermodynamic and transport properties

of the IL/HNO3 mixtures have been determined from equilibrium MD simulations over the entire

composition range (pure IL to pure HNO3) based on bulk simulations. Additional (non-‐equilibrium)

simulations of the composition profile for IL/HNO3 interfaces as a function of time have been

utilized to estimate the composition dependent mutual diffusion coefficients for the mixtures. The

latter have been employed in continuum-‐level simulations in order to examine the nature

(composition and width) of the IL/HNO3 interfaces on the millisecond time scale.

Vaghjiani Ghanshyam

Typewritten Text

DISTRIBUTION A: Approved for public release, distribution unlimited

2

I. Introduction

There is increasing interest in use of room temperature ionic liquids (ILs) as fuels and

propellants. Particularly enticing is the fact that RTILs have negligible vapor pressure, making

them intrinsically much safer than traditional high vapor pressure and toxic fuels such as

hydrazine. While most IL fuels are not hypergolic (i.e., do not spontaneously combust) when mixed

with a liquid oxidizer (e.g., nitric acid), there is a number of energetic ILs that do exhibit

hypergolicity.1 Amongst these are 1-‐butyl-‐4-‐methyl imidazolium [BMIM]/dicyanoamide [DCA],

shown in Figure 1. While [BMIM][DCA] when mixed with HNO3 is hypergolic, [BMIM][NO3-‐] is not.2,3

Understanding the behavior of any hypergolic system is very challenging and complicated due to

the large manifold of reactions involved and the complex interplay between thermophysical

properties and chemical kinetics. When a fuel droplet comes in contact with an oxidizer, some

initial mixing is followed by the exothermic pre-‐ignition reactions that begin to decompose both

fuel and oxidizer, producing various gaseous products. The pathways for these reactions involve

highly reactive transient species that are difficult to detect experimentally. Changes in temperature

and species concentrations due to these reactions as well as the underlying chemical kinetics

themselves are also strongly dependent on physical factors that determine heat and mass transfer

in these systems. Thermophysical properties such as enthalpy of mixing, species inter-‐diffusion,

and thermal conductivity can all play an important role in controlling energy dissipation during the

pre-‐ignition reaction stage.2,4

While thermophysical and transport properties of [BMIM][DCA] and [BMIM][NO3-‐] have

been investigated both experimentally5-‐10 and from MD simulations,11-‐18 there are no data available

about thermophysical properties of these liquids mixed with HNO3. Taking into account that it

usually takes multiple milliseconds for ignition to occur in a hypergolic system there is a significant

3

(from a molecular scale point of view) time period when thermodynamic and thermophysical

processes are dominating the behavior of the mixture and influence the kinetics of initial reactions.

Therefore, we have carried out atomistic molecular dynamics (MD) simulations of

HNO3/[BMIM][DCA] and HNO3/[BMIM][NO3-‐] mixtures for the purposes of better quantifying the

thermophysical properties of these mixtures with the ultimate aim of understanding the nature of

hypergolicity in ILs. Furthermore, modeling of HNO3/[BMIM][DCA], whether at the continuum

level or at the level of detailed liquid-‐phase reaction pathways, will benefit greatly from an

improved understanding of the thermodynamics, structure and transport properties of the mixture.

II. Force Field and Simulation Methodology

MD simulations was performed using the polarizable APPLE&P® force field that has been

developed and extensively validated on a variety of substances including ILs19 and slightly

modified for application to the specific ILs studied here.11 Using this force field our previous

simulations showed very good agreement with experimental thermophysical data for pure

[BMIM][DCA] and [BMIM][NO3-‐] RTILs.11 For the current study the force field for HNO3 was

obtained using our standard procedure, which considered all non-‐bonded interactions and the

dipole polarizability of all atoms to be as transferred from previously calculated quantities for the

nitrate anion, while bond, angular, and dihedral interactions were fit from ab initio data obtained at

the MP2//aug-‐cc-‐pvDz level. Specific details about our fitting procedure can be found in Ref. [19]

while the complete set of force field parameters is available free of charge upon signing a user

license agreement.

MD simulations of bulk [BMIM][NO3-‐]/HNO3 and [BMIM][DCA]/HNO3 mixtures have been

conducted at 333 K and atmospheric pressure using cubic simulation cell (see Fig. 1). Systems with

a composition ranging from 0.0 to 1.0 mol fraction IL in steps of 0.2 have been simulated. The pure

HNO3 system contained 512 molecules while the mixed systems employed 600, 560, 512, or 468

4

total molecules in order of increasing IL mol fraction. Pure IL data was taken from the previous

work, which employed 150 ionic pairs.11 For the mixed systems, the number of ionic pairs

employed were 100, 160, 192, and 208 for the mole fractions studied in increasing IL

concentration. MD simulations were conducted using the molecular simulation package Lucretius

which has the capability to handle polarization effects. Covalent bond lengths were constrained

using the velocity-‐Verlet form of the SHAKE algorithm.20 The Ewald summation method was used

for treatment of long-‐range electrostatic forces between partial atomic charges and between partial

charges and induced dipoles. A tapering function was used to drive the induced dipole/induced

dipole interactions to zero at the cutoff of 10 Å, with scaling starting at 9.3 Å. (The form of the

tapering function is given in the Supporting Information) Induced dipoles were calculated via a

direct iteration with a predictor corrector method. A cutoff of 10 Å was used for all van der Waals

interactions and the real part of electrostatic interactions in the Ewald summation. A multiple time

step reversible reference system propagator algorithm21 was employed. A time step of 0.5 fs was

used for bonding, bending, dihedral, and out-‐of-‐plane deformation motions, while a 1.5 fs time step

was used for non-‐bonded interactions within cutoff radius of 6.0 Å. Finally, the non-‐bonded

interactions in the range between 6.0 and 10.0 Å and reciprocal part of electrostatic interactions

were updated every 3 fs. Each system was initially equilibrated in the NPT ensemble for at least 1

ns, while production runs ranged from 120 to 180 ns depending on the system and temperature.

The length of the production run was chosen to be long enough to allow molecules to reach a

diffusive regime (when the ion mean squared displacement shows a linear time dependence,

MSD(t) ~ t), therefore allowing an accurate estimation of the self-‐diffusion coefficients.

In addition to equilibrium bulk simulations of IL/HNO3 mixtures described above we also

conducted MD simulations at non-‐equilibrium conditions in which we monitor the process of

intermixing of IL and HNO3 liquids. To conduct these simulations a liquid-‐liquid interface has to be

set up as also shown in Figure 1 where RTIL and oxidizer are well separated. Several adjustments

5

to the simulation protocol have been implemented to allow these types of simulations. First, since

IL and oxidizer are miscible the preparation of initial configuration that allows sharp yet tight (no

vacuum) interface between IL and oxidizer has to be prepared. To create a sharp liquid-‐liquid

interface we modify parameters for van der Waals interactions between IL and oxidizer molecules

to make them more repulsive. Specifically, we set dispersion parameters Cij (of the term –Cij/r6) to

zero for all cross-‐terms interactions between the IL and oxidizer. This simple modification was

enough to provide a sharp interface between liquids without creating any additional artifacts to

bulk materials away from the interface. Using this approach, initial configurations can be

equilibrated for any period of time and then switched to simulations with realistic force field for

production runs sampling the intermixing rate. In these simulations, the simulation cell dimensions

were 35 X 35 X 140 Å with the larger dimension being perpendicular to the interface. Systems

contained approximately the same volume of IL and oxidizer. During these simulations the

pressure (stress tensor) was controlled separately in each direction, allowing the simulation to

account for changes in pressure associated with mixing of the components. Simulations were

conducted at 333 K and atmospheric pressure control along the large dimension (perpendicular to

the interface). Two other dimensions were fixed at 35x35.

III. Simulations of Bulk Mixtures

A. Structure

We began our analysis of the HNO3/IL mixtures by investigating liquid-‐phase structure as a

function of mixture composition. Figures 2a-‐b show center-‐of-‐mass BMIM-‐BMIM radial

distribution functions g(r) as a function of separation r for HNO3/[BMIM][DCA] and

HNO3/[BMIM][NO3-‐] mixtures for the various compositions investigated. It can be seen that for

both systems there is a tendency for non-‐ideal mixing, i.e., the structure of the solution depends

somewhat upon composition. For both mixtures the position of the first peak in the BMIM-‐BMIM

6

g(r) moves to greater separation with increasing dilution (by HNO3). For HNO3/[BMIM][DCA] the

magnitude of the first peak also decreases with increasing dilution. The behavior observed in

Figure 2 might be associated with strong BMIM-‐HNO3 interactions, but Figure 3, which show the

BMIM-‐HNO3 radial distribution functions for the two mixtures at selected compositions, indicate

that this is not the case. For the HNO3/[BMIM][DCA] mixtures a slight decrease (as opposed to an

expected increase) in the magnitude of the first peak in the BMIM-‐HNO3 radial distribution function

with dilution by HNO3 can be seen. Both mixtures show near ideal mixing behavior with respect to

BMIM-‐HNO3 interactions, i.e., very little composition dependence is observed in the radial

distribution functions.

We have also investigated the role of HNO3 on interactions between cations and anions in

the mixtures by examining the cation-‐anion radial distribution functions as shown Figures 4a,b for

HNO3/[BMIM][DCA] and HNO3/[BMIM][NO3-‐], respectively. The latter shows remarkably little

influence of the oxidizer on cation-‐anion correlation in [BMIM][NO3], while the former indicates

that introduction of HNO3 promotes stronger nearest-‐neighbor (first radial distribution function

peak) interaction between BMIM and DCA. Examination of the anion-‐oxidizer radial distribution

functions, shown in Figures 5, shows very little dependence of the nature of the DCA/HNO3

interaction on composition, while NO3-‐ /HNO3 interactions become somewhat stronger with

increasing dilution. These effects are manifested in DCA-‐DCA pair distribution functions that are

essentially independent of composition while NO3-‐/NO3-‐ correlations decrease notably with

increasing HNO3 content, as shown in Figures 6a-‐b.

From the magnitude of the first peaks in the radial distribution functions, it is clear that the

oxidizer interacts more strongly with the anions (DCA or NO3-‐) than with the BMIM cation.

Interestingly the first peak in the HNO3/NO3-‐ radial distribution function is high and narrow,

indicating a strong preference for specific distance and/or orientations, while that for HNO3/DCA is

7

quite broad, indicating less structure in this interaction. Atomically, the preferred interaction

between HNO3 and NO3-‐ is between the acidic proton and the oxygen atoms of the anion, while for

HNO3 and DCA the preferred interaction is between the acidic proton and the (terminal) nitrogen

atoms of the cyano groups. The H(acidic)-‐O(anion) and H(acidic)-‐N(cyano) atomic radial

distribution functions are shown in Figure 7. Interestingly, remarkably little dependence of these

interactions on the composition of the solution is observed. All radial distribution functions show a

sharp, high peak at a separation of around two Å. We note that the force field employed in the

simulations does not allow for transfer of the proton between species, so the nature of this

interaction (e.g., minimum energy position/radial distribution function peak position) is driven

entirely by physical (van der Waals and electrostatic) interactions. Integration of the radial

distribution functions and multiplication by the appropriate densities yields the running

coordination number of acidic protons near O(anion) or N(cyano) as shown in Figure 7c. We take a

separation of 2.9 Å (see Figures 7a-‐b) as corresponding to the first coordination shell of acidic

protons hear O(anion) or N(cyano). As expected, the number of acidic hydrogen atoms

coordinating each O(anion) or N(cyano) increases with increasing dilution. For the XIL = 0.2

solutions (80 mol% HNO3) the NO3-‐ oxygen atoms and DCA cyano nitrogen atoms are fully

coordinated, i.e., there is more than one on average of acidic hydrogen atoms in the first

coordination shell of these atoms.

B. Density, Volume of Mixing and Heat of Mixing

The density and excess volume for the two HNO3/IL mixtures from simulations are shown

in Figures 8a-‐b as a function of composition. The density of the pure ionic liquids are 1.030 g/cm3

and 1.137 g/cm3 for [BMIM][DCA] and [BMIM][NO3-‐], respectively. These values are in a good

agreement with experimental values of 1.041 g/cm3 for [BMIM][DCA]6 and 1.131 g/cm3 for

[BMIM][NO3-‐]7 with 0.5% and 1.1% deviation, respectively. The simulated density of the pure HNO3

8

at 298 K is 1.45 g/cm3, compared with an experimental density22 of 1.51 g/cm3. Mixing of the ILs

with increasing concentration of oxidizer results in a monotonic increase in density. Examination

of the excess volume of mixing shows minimal deviation from ideal mixing behavior, particularly

for the HNO3/[BMIM][NO3-‐] system. Figure 8c shows the enthalpy of mixing as a function of

composition for both IL mixtures. Both exhibit exothermic behavior, with the HNO3/[BMIM][NO3-‐]

system showing stronger exothermic character. Combined with the near-‐ideal entropy of mixing

(configurational entropy) behavior revealed by the intermolecular radial distribution functions

above, we can anticipate that both of these ILs are consoluble with HNO3. It is also clear that the

temperature of the systems will increase upon adiabatic mixing, which is an important (if not

crucial) aspect for onset of ignition in hypergolic mixtures. The extent of adiabatic heating for these

mixtures is addressed in Section IV.

C. Self-diffusion Coefficients

The rate at which a liquid fuel and oxidizer intermix is important in determining the

hypergolic character of the mixture. While intermixing dynamics are investigated in more detail

below, it is instructive to examine the self-‐diffusion coefficients of the IL components and the

oxidizer as a function of mixture composition as shown in Figure 9. Figure 9 reveals that ion self-‐

diffusion rates are significantly greater in [BMIM][DCA] than in the [BMIM][NO3-‐], consistent with

the relative viscosities of these ILs with [BMIM][NO3-‐] being about factor 4 more viscous than

[BMIM][DCA] at 333K.6,23 The HNO3 liquid has a much lower viscosity/greater self-‐diffusion

coefficient than the ILs, hence, dilution of the ILs with HNO3 results in a monotonic increase in ion

self-‐diffusion coefficients and monotonic decrease in HNO3 diffusion coefficient. The composition

dependence of the ion and HNO3 diffusion coefficients is greater in the HNO3/[BMIM][NO3-‐] mixture

than observed in HNO3/[BMIM][DCA] mixture. To first order this is consistent with the greater

9

difference in self-‐diffusion coefficients of HNO3 (fast) compared to the IL (slow) in the former

system compared to the latter.

IV. Simulation of Ionic Liquid/Oxidizer Mixing

In addition to analysis of bulk properties under equilibrium conditions discussed above we have

investigated properties of mixtures during the mixing process. Below we discuss the analysis of

interdiffusion and adiabatic heating processes upon mixing.

A. Diffusion

Fig. 10a shows the concentration profile for HNO3 and the IL the HNO3/[BMIM][DCA]

system after 200 ps of mixing and after 3.5 ns of mixing, while Fig. 10b shows the composition

profile after the same periods. Similarly, Fig. 11a shows the concentration profile for HNO3 and the

IL the HNO3/[BMIM][NO3-‐] system after 200 ps of mixing, after 3.0 ns of mixing and after 5.9 ns of

mixing, while Fig. 11b shows the composition profile after the same periods. Each profile is an

average of three profiles (e.g., the 200 ps profiles are averages of profiles at 100 ps, 200 ps and 300

ps). Examination of Figs. 10 and 11 show obvious asymmetry in mixing at the interface, indicating

that the mutual diffusion coefficient DAB (A = oxidizer, B = IL) is strongly composition dependent for

both mixtures. A typical diffusion coefficient in these mixtures might be on the order of 1x10-‐9 m2/s

(see Fig. 9), implying mixing on a nanometer length scale on a nanosecond time scale, consistent

with behavior observed in Figs. 10 and 11.

The governing equation for mutual diffusion (Fick’s second law) in one spatial dimension is

given as24

€

∂cA (r,t)∂t

=1rm

∂∂r

rmDAB (XA )∂cA (r,t)∂r

⎛

⎝ ⎜

⎞

⎠ ⎟ (1)

10

€

∂cB (r,t)∂t

=1rm

∂∂r

rmDAB (XA )∂cB (r,t)∂r

⎛

⎝ ⎜

⎞

⎠ ⎟ (2)

€

XA =cA (r,t)

cA (r,t) + cB (r,t) (3)

where m = 0 for the slab geometry and 2 for spherical geometry. The dependence of DAB on

composition is a priori unknown and there is no robust theory for predicting DAB(XA). However, it

has been observed that the following relationship

€

logDAB = logDB + XA (logDA − logDB ) (4)

where DA and DB are the pure component self-‐diffusion coefficients works well in some materials.

Note that the self-‐diffusion coefficients of the species in the mixtures tend to follow (at least

reasonably) this relationship (see Fig. 9). Using the profiles at 200 ps as initial conditions, we

employed eqs. 1-‐4 to predict the concentration and composition profiles for both mixtures.

Comparisons can be seen in Figs. 10 and 11, indicating that eq. 4 provides a reasonable description

of the composition dependence of DAB. Here we took the self-‐diffusion coefficient of pure HNO3

from Figure 9 and used the average of the cation and anion self-‐diffusion coefficients for the pure IL

self-‐diffusion coefficients, again taken from Figure 9.

Once the composition dependence of the mutual diffusion coefficient is known, it is possible

to utilize eqs. 1-‐4 with suitable initial and boundary conditions to prediction the

concentration/composition profiles for any geometry of interest after any time of interest. For

example, Fig. 12 shows the interfacial composition for a 2.5 mm radius droplet of [BMIM][DCA] and

[BMIM][NO3-‐], respectively, in a sea of HNO3 oxidizer, after periods of 10 and 100 ms. For both

mixtures the interfacial region is on the order of microns in thickness as expected given the

magnitude of the mutual diffusion coefficient (eq. 4). It is notable that on these time scales the

width of the interfacial region is not significantly larger for the HNO3/[BMIM][DCA] mixture than

11

for the HNO3/[BMIM][NO3-‐] mixture, despite the fact that the self-‐diffusion coefficient for

[BMIM][DCA] is almost four times greater than that for [BMIM][NO3-‐]. However, if we utilize an

imaginary “fast” oxidizer with a self-‐diffusion coefficient four times that of HNO3, mixing with

[BMIM][NO3-‐] on these time scales occurs much more rapidly, as shown in Figure 12.

B. Adiabatic Heating

Heat generation upon mixing is another important property that can influence kinetics of

initial reactions and, hence, the hypergolicity of the mixture. Two approaches were applied for

calculating heat generation due to mixing. First, calculations were based on bulk mixture heat of

mixing data (see Section III.B). If one knows the heat of mixing for the mixture of two components

(i.e., IL and oxidizer) then the heat generated upon their mixing can be estimated knowing the final

composition of the mixture. For example, for the [BMIM][DCA]/HNO3 system with composition

used in non-‐equilibrium simulations (XIL = 0.23) we estimate about 17 degrees temperature

increase. For [BMIM][NO3]/HNO3 with similar composition the corresponding heating is estimated

to be about 45 degrees.

Alternatively one can conduct brute force simulations of mixing process in the NVE

ensemble and directly measure how much the system heats up. While conceptually this method is

straightforward, special care must be taken to control the integration uncertainty, which can

otherwise lead to additional heat generation due to Hamiltonian drift. The latter can be measured

by conducting simulations of a completely mixed state using the same simulation set

up/parameters as in production run. A relatively short run (300-‐500ps) provides a good estimate

of the rate of the Hamiltonian drift (if any) that can be then taken into account (subtracted) in the

analysis of the production mixing simulation. Using this approach and applying correction for the

Hamiltonian drift, a 17 degree heating was obtained from the non-‐equilibrium simulation of

[BMIM][DCA]/HNO3 mixing, consistent with the estimate from bulk simulations discussed above.

12

Similarly, the heating in [BMIM][NO3]/HNO3 system was found to be 45 degrees which is also

consistent with the estimate from bulk simulations.

These simulations/estimations of heat generation due to physical mixing show that the

heating is modest. In principle, taking into account that HNO3 vaporization temperature is 353 K

then even 20-‐40 degrees heating can be important. However, it is important to realize that the

relatively narrow intermixing region is surrounded by the large amount of pure IL and oxidizer

phases that can serve as heat sinks. In this case, the heating of the mixed layer will strongly depend

on the interplay between thermal and molecular diffusivities in the system. The latter can be

characterized by the Lewis number (Le) and is the ratio of the thermal diffusivity of a fluid, given as

α = κ/(Cp*ρ), to the molecular diffusivity. Taking into account typical values for thermal

conductivity (κ), heat capacity (Cp), and density (ρ) reported in the literature for IL25 and nitric

acid26 we can estimate α for our mixture components. The thermal diffusivity of nitric acid is

around 9x10-‐8 m2/s, while that for a number of various ILs is in the range of 6x10-‐8 m2/s. Hence,

unlike molecular (mutual or self) diffusivity, we anticipate that the thermal diffusivity of the ionic

liquid/nitric acid mixture will not depend strongly on composition, and will be on the order of

6x10-‐8 m2/s. Using a representative diffusion coefficient of the IL/nitric mixtures of 1x10-‐9 m2/s

(which is on the high side of the range), we estimate Le ≥ 60. Hence, for viscous fluids such as ILs

investigated here, the time scale of thermal diffusion is much less than that of mass diffusion. Even

for nitric acid itself we estimate Le ~ 10.

This analysis indicates that it is unlikely that any noticeable local temperature rise can be

expected in the interfacial region due to heat of mixing. In our brute force mixing simulations we

have analyzed the local temperature profile after 200-‐500ps. On these time scales, IL and HNO3

have only intermixed in a relatively small region of 2nm wide. If the thermal dissipation would be

much slower than molecular diffusion then we should observe an increase of temperature in the

13

intermixed region due to heat of mixing. However, neither of two mixtures showed any indication

of increased temperature in the intermixed region compared to the rest of the system, indicating

that the thermal energy generated due to mixing quickly dissipates to IL and HNO3 phases and

results in homogeneous heating of the entire system.

V. Conclusions

Atomistic molecular dynamics simulations of HNO3/[BMIM][NO3-‐] and HNO3/[BMIM][DCA]

mixtures using polarizable force field revealed a complete consolubility for both systems in the

entire range of concentrations. Both mixtures exhibited exothermic behavior, with the

HNO3/[BMIM][NO3-‐] system showing stronger exothermic character. Analysis of various pair

correlations functions showed very little dependence on mixture composition indicating a near-‐

ideal entropy of mixing. Analysis of the liquid structure revealed that the most prominent difference

between two mixtures is in the anion-‐HNO3 correlations. The first peak in the HNO3/NO3-‐ radial

distribution function is high and narrow, indicating a strong preference for specific distance and/or

orientations, while that for HNO3/DCA is quite broad, indicating less structure in this interaction.

However, in both systems the potential anion proton acceptor atoms (oxygens for NO3-‐ and

nitrogens in DCA) are well coordinated by acidic hydrogen at all investigated compositions

indicating that there no structural hindrances for initial anion protonation reactions to occur.

Analysis of molecular diffusivity showed a significant speed up of mobility of ions upon

dilution with nitric acid. We found that molecular interdiffusion obtained from brute force

simulation of mixing IL and oxidizer can be accurately described by a simple diffusion equation

utilizing parameters obtained from MD simulations and simple empirical relation for calculation of

mutual diffusion coefficients. The developed continuum level analytical model allowed us to

estimate concentration profiles on time and length scales relevant to hypergolic ignition (multiple

14

ms and µm) but are well outside of accessibility range for brute force atomistic MD simulations.

Our analysis indicates that despite quite different diffusivity/viscosity between two investigated ILs

their intermixing with nitric acid is quite similar on time scales of 10-‐100ms. Finally, the analysis of

adiabatic heating upon mixing IL and oxidizer revealed that the released enthalpy of mixing is

sufficient to allow a noticeable heating in the intermixed region. However, due to intrinsically high

thermal diffusivity (compared to molecular diffusivity) of IL and nitric acid all heat generated in the

intermixed layer is quickly dissipating to non-‐mixed regions. Taking into account that on time

scales 10-‐100ms only a small fraction of a fuel droplet has intermixed with an oxidizer and hence

the dominating non-‐mixed regions of IL and oxidizer can quickly sink the heat generated in the

intermixed region. Therefore, no noticeable temperature increase due to heat of mixing can be

expected in the intermixing region.

VI. Acknowledgment

We are grateful for the financial support of this work by the Air Force Office of Scientific Research

and through the SBIR program (contract number FA9300-11-C-3012) to Wasatch Molecular Inc.

Opinions, interpretations, conclusions, and recommendations are those of the authors and are not

necessarily endorsed by the United States Government.

15

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Figure Captions.

Figure 1. Chemical structure of ions and nitric acid as well as snapshots from equilibrium bulk

simulation and non-‐equilibrium mixing simulation of [BMIM][DCA]/nitric acid system.

Figure 2. BMIM-‐BMIM radial distribution functions for HNO3/[BMIM][DCA] (a) and

HNO3/[BMIM][NO3-‐] (b) mixtures.

Figure 3. BMIM-‐HNO3 radial distribution functions for HNO3/[BMIM][DCA] and HNO3/[BMIM][NO3-‐

] mixtures at selected compositions.

Figure 4. Cation-‐anion radial distribution functions for HNO3/[BMIM][DCA] (a) and


Figure 5. Anion-‐HNO3 radial distribution functions for HNO3/[BMIM][DCA] and HNO3/[BMIM][NO3-‐

] mixtures at selected compositions.

Figure 6. Anion-‐anion radial distribution functions for HNO3/[BMIM][DCA] (a) and


Figure 7. The H(acidic)-‐O(anion) and H(acidic)-‐N(cyano) atomic radial distribution functions for

HNO3/[BMIM][NO3-‐] (a) and HNO3/[BMIM][DCA] (b), along with the corresponding running

coordination numbers (c).

Figure 8. Density (a), excess volume (b) and heat of mixing (c) for HNO3/[BMIM][DCA] and

HNO3/[BMIM][NO3-‐] mixtures as a function of composition.

Figure 9. Ion and oxidizer self-‐diffusion coefficients as a function of mixture composition for

HNO3/[BMIM][DCA] and HNO3/[BMIM][NO3-‐] mixtures.

18

Figure 10. Time-‐dependent composition (a) and concentration (b) profiles for the

HNO3/[BMIM][DCA] slab system after 200 ps and 3.5 ns of mixing.

Figure 11. Time-‐dependent composition (a) and concentration (b) profiles for the

HNO3/[BMIM][NO3-‐] slab system after 200 ps, 3.0 ns and 5.9 ns of mixing.

Figure 12. Interfacial profiles for a 2.5 mm radius sphere of [BMIM][DCA] or [BMIM][NO3-‐]

(indicated by arrows) in a sea of HNO3 predicted by using eqs. 1-‐4. The “fast” oxidizer system

shows mixing of [BMIM][NO3-‐] with an oxidizer than has a self-‐diffusion coefficient four times that

of HNO3.

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Figure 1.

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Figure 2.

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Figure 3.

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Figure 4.

23

Figure 5.

24

Figure 6.

25

Figure 7

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Figure 8

27

Figure 9.

28

Figure 10.

29

Figure 11.

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Figure 12.

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